Method for receiving spectrum spreading signals with frequency shift correction

ABSTRACT

A method for receiving spectrum spreading signals using a Doppler-effect frequency-shift correction generates a corrective signal based on an estimation of a modulation period related to the Doppler effect detected in a preamble portion of a received signal. The corrective signal is used for correcting an information portion of the received signal. Base band digital signals are operated upon by using the DOT and CROSS components.

TECHNICAL FIELD

The object of the present invention is a method for receiving spectrum spreading signals with frequency shift correction. It finds an application in digital transmissions.

With the invention, effects due to untimely frequency shifts may be corrected, regardless of the origin of these shifts. Most often, this will be a Doppler effect related to the moving speed of the receiver. But this might also be effects due to a frequency shift of the local oscillators. In the description which follows, it will be assumed that the effect to be corrected is a Doppler effect, without however limiting the scope of the invention to this case.

PRIOR STATE OF THE ART

A great number of publications have been made on the correction of the Doppler effect. For example, patent U.S. Pat. No. 5,007,068 may be mentioned as well as the corresponding article of M. K. SIMON and D. DIVSALAR entitled “Doppler-Corrected Differential Detection of MPSK”; published in the journal, “IEEE Transactions on Communications”, Vol. 37, No. 2, February 1989, pages 99-109. These documents describe a technique wherein the Doppler shift is determined on one half of the symbol period. For this purpose, the receiver uses two circuits each with a half period delay, and a Doppler effect estimation circuit connected between the two delay circuits. The correction is then performed on the usual demodulated signal.

This technique may also be used for modulations of the multiple differential phase modulation type (abbreviated as MDPSK for “M-ary Differential Phase Shift Keying”), but it is not applicable to spectrum spreading transmissions where each symbol is multiplied by a pseudo-random sequence.

The article of F. D. NATALI, entitled “AFC Tracking Algorithms”, published in the journal, “IEEE Translations on Communications, vol. COM-32, No. 8, August 1984, pages 935-947, describes a technique in which preambles made up of known symbols are formed before transmitting the useful information. The working frequency is automatically controlled (“Automatic Frequency Control” or AFC) by a loop structure.

This technique is not adapted to the case when information data blocks separated by blanks are transmitted.

The following correction techniques may further be mentioned:

-   -   the use of double detection, which gets rid of the Doppler         effect by suitable encoding (U.S. Pat. No. 4,481,640);     -   the use of the frequency mixing principle in the radio portion         of the receivers (U.S. Pat. No. 4,706,286);     -   the use of a phase locked loop (PLL) in the radio portion (U.S.         Pat. No. 4,841,544);     -   the use of a dual mode with increased throughput (U.S. Pat. No.         5,623,485).

These techniques are generally expensive and complex and do not make the most out of the advantages of spectrum spreading, nor of the digital processing of the signals. The object of the present invention is precisely to overcome these drawbacks by providing a method which processes the signals in the base band (and not the signals in the radio portion) and which is well adapted to digital processing.

Document EP-A-0 822 668 describes a receiver for spectrum spreading signals wherein the Doppler effect correction is performed on the base band signal.

DESCRIPTION OF THE INVENTION

Specifically, the object of the invention is a method for receiving spectrum spreading signals with frequency shift correction, wherein:

-   -   a signal is received comprising a preamble made up from a         sequence of known symbols spread in frequency by a pseudo-random         sequence, followed by a sequence of information symbols spread         in frequency by said pseudo-random sequence,     -   a base band signal is formed from the received signal,     -   a correlation is performed between the base band signal and the         pseudo-random sequence at least in the portion of the signal         corresponding to the information symbols, in order to obtain a         correlation signal,     -   a demodulation of the correlation signal is performed in order         to obtain a demodulation signal,     -   the information symbols are restored,         a method wherein the frequency shift correction comprises the         following steps:     -   a. in a first step, the demodulation signal is processed in the         portion corresponding to the preamble, in order to estimate the         period of the modulation affecting the signal because of the         frequency shift and a correcting signal with this estimated         period is elaborated,     -   b. in a second step, the signal is corrected before or after the         correlation in the portion corresponding to the information         symbols, by means of said correcting signals,         the method being characterized in that:     -   the base band signal is divided into two components, a first         -component (I) and a second component (Q) in quadrature with the         first and a correlation is performed on each of these components         in order to obtain two correlation components CORR (I) and CORR         (Q),     -   a DOT signal is calculated which is the sum of two direct         products of successive samples of the correlation components,         and a CROSS signal is calculated which is the difference between         two crossed products of successive samples of the correlation         components,     -   in order to estimate the period (T) of the modulation, the ratio         between a CROSS signal and a DOT signal is calculated at each         symbol period, the arc is calculated for which the tangent is         equal to this ratio, the inverse of this arc is calculated and         multiplied by πN/2.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a reminder of the general structure of a spreading spectrum signal receiver;

FIG. 2 shows a correlation signal corresponding to a signal not affected by the Doppler effect;

FIG. 3 shows this same signal affected by a slight Doppler effect;

FIG. 4 shows this same signal but with a very strong Doppler effect;

FIG. 5 illustrates the sinusoidal modulation affecting a correlation signal because of the Doppler effect and it shows the period T of this modulation;

FIG. 6 is a block diagram showing the estimation of the Doppler modulation from the DOT and CROSS demodulation signals;

FIG. 7 illustrates an embodiment of a unit for estimating the modulation period and for forming the correction signal for the Doppler effect;

FIG. 8 illustrates an embodiment of a correction circuit for the Doppler effect;

FIGS. 9A and 9B show a correlation signal before and after correction for the I channel;

FIGS. 10A and 10B show a correlation signal before and after correction for the Q channel;

FIGS. 11A and 11B show a correlation signal before and after correction on the I channel, with Gaussian noise;

FIGS. 12A and 12B show a correlation signal before and after correction on the Q channel, with Gaussian noise;

FIG. 13 schematically illustrates the structure of a receiver with parallel suppression of interferences and weighting, with Doppler effect correction according to the invention;

FIG. 14 shows the variations of the bit error rate versus the signal to noise ratio and enables the performances of a receiver according to the invention to be compared with other receivers of known types.

DESCRIPTION OF THE PARTICULAR EMBODIMENTS

FIG. 1 is a reminder of the general structure of a direct sequence spectrum spreading signal receiver. As an example, it is assumed that the modulation carried out at emission is a phase difference modulation. The receiver comprises means not shown such as an antenna and means for switching to base band, i.e. in order to multiply the received signal by a signal with the frequency of the carrier. The receiver generally includes two parallel channels, marked by indices I and Q, for the processing of a signal in phase with the carrier and a signal in phase quadrature with the latter. The illustrated receiver thus comprises two inputs E(I), E(Q), two analog-digital converters ADC(I), ADC(Q), two circuits F(I), F(Q) delivering two CORR(I) and CORR(Q) signals, a differential demodulation (DD) circuit delivering two signals, conventionally marked as “DOT” and “CROSS” (which are sums or differences of sample products at the correlation output), a circuit Inf/H restoring an information signal Sinf and a clock signal SH, and finally a decision circuit D, the output of which restores data d.

Circuits F(I), F(Q) perform a correlation operation between the received signal and the pseudo-random sequence used at emission. This operation consists in storing a certain number of successive samples and in performing a weighted sum with the help of coefficients which are the coefficients for direct sequence spectrum spreading. These coefficients are equal to +1 and to −1, according to the sign of the chips forming the pseudo-random sequence.

The analog-digital converters ADC(I) and ADC(Q) operate at frequency n_(e)F_(c) where F_(c) is the frequency of the chip (F_(c)=1/T_(c)), and n_(e) is the number of samples taken in a chip period (T_(c)). To simplify the discussion, it will be assumed that one sample is taken per chip. The correlation signals CORR(I) and CORR(Q) contain one correlation peak per symbol period.

As for the DOT and CROSS signals delivered by the demodulation circuit DD, as a reminder, they are for the first, the sum I_(k)I_(k−1)+Q_(k)Q_(k−1) and for the second, the difference Q_(k)I_(k−1)−I_(k)Q_(k−1), where I_(k) and Q_(k) designate the correlation samples of rank k for channels I and Q, the rank corresponding to a symbol period (I_(k) corresponds to CORR (I_(k)) and Q_(k) to CORR (Q_(k))).

FIG. 2 shows the sequence of the correlation peaks in the ideal case of a preamble made up of binary data each equal to +1, the transmission being not affected by a Doppler effect. FIG. 2 relates both to channel I and channel Q. The time counted in chip periods appears on the abscissa. These peaks are separated from each other by N chips. In the illustrated case, N=31. All the peaks have the same amplitude, in the ideal case, without any noise.

FIG. 3 illustrates the same case, but with a slight Doppler effect, while FIG. 4 illustrates the case of a strong Doppler effect. The frequency shift due to the Doppler effect is expressed by a phase shift of the processed signal and by a parasitic modulation of the correlation signal.

FIG. 5 resumes this matter in a more accurate way and shows the modulation related to the perturbation with its half-period marked as T,. which is the time (counted in the number of chips) separating two successive extrema. The total period of the parasitic modulation is therefore equal to 2T. The method of the present invention enables this parasitic modulation to be corrected. According to the invention, this is carried out in two steps: first of all, the period T (or its double 2T) is measured, so that a correction signal may be elaborated; then the signals are corrected by said correction signal.

In order to estimate the time T (or 2T), according to the invention, the correlation signals are used as DOT and CROSS signals.

To carry out the correction, either the incident signals or the correlation signals are acted upon. There are therefore several possible alternatives which are illustrated in FIGS. 6-8. In these figures, the notations have been slightly changed with respect to those of FIG. 1, in the sense that the signals before their processing bear a “DOP” index, to notify that they are affected by Doppler effect, the signals after processing being cleared of this index.

In FIG. 6, the Doppler effect estimation circuit EST_(dop) processes demodulation signals DOT_(dop)(I) and/or CROSS_(dop)(Q). Correction is carried out either on I_(dop) and Q_(dop), or on CORR_(dop)(I) and CORR_(dop)(Q), in circuit CC_(dop).

The properties of the signals to be processed are used for determining the period T illustrated in FIG. 5 (or 2T). Indeed, it may be considered that the correlation signals corresponding to a preamble are made up of the samples of a cosine wave and of a sine wave of a half-period T, sampled every kN chips (cf. FIG. 5). This may therefore be written as: CORR_(dop)(I _(k))=P.cos(πkN/2T)   (1) CORR_(dop)(Q _(k))=P.sin(πkN/2T)   (2) where P is an amplitude.

After differential demodulation, the following DOT and CROSS signals are obtained: DOT_(dop)(k)=CORR_(dop)(I _(k)).CORR_(dop)(I _(k−1))+CORR_(dop)(Q _(k)).CORR_(dop)(Q _(k−1))   (3) CROSS_(dop)(k)=CORR_(dop)(Q _(k)). CORR_(dop)(I _(k−l))−CORR_(dop)(I _(k)).CORR_(dop)(Q _(k−1))   (4) By replacing in (3), (4) the quantities with their values given by (1) and (2) and taking into account the properties of trigonometric functions, it is found that: DOT_(dop)(k)=P ².cos(πN/2T)   (5) CROSS_(dop)(k)=P ².sin(πN/2T)   (6) It is seen that both DOT_(dop) and CROSS_(dop) quantities are independent of the rank k of the preamble symbol.

By taking the ratio of these quantities, the tangent of angle πN/2T is formed from which the angle and the value of T may be extracted: $\begin{matrix} {T = \frac{\pi \cdot {N/2}}{\tan^{- 1}\left( \frac{{CROSS}_{dop}(k)}{{DOT}_{dop}(k)} \right)}} & (7) \end{matrix}$ where tan⁻¹(.) means “arc for which the tangent is equal to (.)”.

The Doppler effect estimation circuit EST_(dop) of FIG. 6 is therefore simply a circuit comprising a divider for signals A=CROSS_(dop)and B=DOT_(dop), a circuit for calculating tan⁻¹(A/B), an inverter and a multiplier by Nπ/2. T being known, a correction signal needs to be generated for which one component Cc is a cosine and the other Cs a sine: Cc=cos(πx/2T)   (8) Cs=sin(πx/2T)   (9) Such a signal is generated by a generator with two quadrature outputs.

This calculation may be changed by taking a sequence of weighted samples and calculating: $\begin{matrix} {T = \frac{\pi \cdot {N/2}}{\tan^{- 1}\left\lbrack \frac{\left( {1 - \alpha} \right) \cdot {\sum\limits_{k = 0}^{\infty}{\alpha^{k}{{CROSS}_{dop}(k)}}}}{\left( {1 - \alpha} \right) \cdot {\sum\limits_{k = 0}^{\infty}{\alpha^{k}{{DOT}_{dop}(k)}}}} \right\rbrack}} & (10) \end{matrix}$ Still in a more general way, estimation of T is improved by proceeding with low pass filtering of signals DOT_(dop) and CROSS_(dop), i.e., with A=f(CROSS_(dop)(k)) and B=f(DOT_(dop)(K)), where f represents the filtering function: $\begin{matrix} {T = \frac{\pi \cdot {N/2}}{\tan^{- 1}\left\lbrack \frac{A}{B} \right\rbrack}} & (11) \end{matrix}$ A generator receiving T, delivers components Cs and Cs as defined by (8) and (9).

FIG. 7 illustrates a particular embodiment of the estimation circuit. This circuit comprises two amplifiers 10, 11 with gain (1-α), two multipliers 12, 13, the output of which is fed back to a second input as a loop by an amplifier 14, 15 via a delay line 16, 17. The circuit is completed by means for applying the relation (11), i.e., a divider 20, a circuit 22 for calculating the arc tangent, a circuit 24 which calculates the inverse of the arc tangent, and an amplifier 26 with gain πN/2 which delivers quantity T. A generator 30 receiving T delivers components Cc and Cs as defined by (8) and (9).

Having described the means for obtaining both components Cc and Cs of the correction signal, a description will now be made on how the received signals are corrected accordingly. This correction processes the signals carrying the transmitted information and no longer the preamble.

Generally, the correlation signals CORR(I) and CORR(Q) of the phase and quadrature channels may be considered as real and imaginary components of a complex signal CORR(I)+jCORR(Q). The Doppler effect changes the phase of this signal (in other words, it rotates the vector which represents it) by a quantity e^(j(πx/2T)). The obtained signal is the Doppler effect affected signal. Its components are CORR_(dop)(I) and CORR_(dop)(Q). This may be therefore written as: CORR_(dop)(I)+jCORR_(dop)(Q)=[CORR(I)+jCORR(Q)]e ^(j(πx/2T))   (12 Conversely, the components free from the Doppler effect may be expressed with respect to the components impaired by the Doppler effect as: CORR(I)+jCORR(Q)=[CORR_(dop)(I)+jCORR_(dop)(Q)]e ^(−j(πx/2T))   (13)

By developing the right-hand member of this equation and by identifying the real and imaginary terms, it is found that: CORR(I)=CORR_(dop)(I).cos(πx/2T)+CORR_(dop)(Q).sin(πx/2T)   (14) CORR(Q)=CORR_(dop)(Q).cos(πx/2T)−CORR_(dop)(I).sin(πx/2T)   (15)

The same relationships may be established with signals I and Q, i.e.: [I+jQ]=[I _(dop) +jQ _(dop) ]e ^(−j(πx/2T))   (16) i.e.: I=I _(dop).cos(πx/2T)+Q _(dop).sin(πx/2T)   (17) Q=Q _(dop).cos(πx/2T)−I _(dop).sin(πx/2T)   (18) The correction circuit must therefore comprise multipliers for multiplying the signals to be corrected by both components of the correction signal, and adders in order to perform the sum of the obtained products. FIG. 8 shows an example of such a circuit. As illustrated, it comprises two multipliers 41 and 42 receiving I_(dop) or CORR_(dop)(I) and cos(πx/2T) for the first and Q_(dop) or CORR_(dop)(Q) and sin(πx/2T) for the second, respectively, and an adder 43 connected to both multipliers in order to deliver the signal from the first channel corrected from the Doppler effect, i.e., I or CORR(I). Similarly, the circuit further comprises two multipliers 51 and 52 receiving Q_(dop) or CORR_(dop)(Q) and cos(πx/2T) for the first and I_(dop) or CORR_(dop)(I) and sin(πx/2T) for the second, respectively, and an adder 53 with an inverting input (in other words a subtractor), the inverting input being connected to multiplier 52 and the other input to multiplier 51. This adder 53 delivers the signal of the second channel corrected from the Doppler effect, i.e., Q or CORR(Q)

FIGS. 9A, 9B and 10A, 10C, on the one hand, as well as 11A, 11B and 12A, 12B, on the other hand, illustrate the correction which has just been described.

In FIG. 9A, first of all, a correlation signal of channel I is seen before correction and affected by a Doppler effect. In FIG. 9B, this effect has been corrected.

In FIGS. 10A and 10B, the same signals are seen before and after correction, but on channel Q.

FIGS. 11A, 11B and 12A, 12B show the same signals but in the presence of noise such that a signal to noise ratio is 5 dB.

The invention is not limited to the case when both channel I and channel Q are corrected. One or the other of these channels might as well be corrected. The correction circuit will then implement the portion of the means required for calculating expressions (18) or (19).

The invention, which has just been described, is applied to any type of pseudo-random sequence spectrum spreading signal receiver. In particular it may be applied to so-called Code Division Multiple Access (CDMA) transmissions. In these transmissions, several users share a same channel by means of different pseudo-random sequences. The receiver then comprises as many parallel channels as users. In a particular embodiment, such a CDMA receiver may comprise parallel suppression means for interference between users, with weighting means. Such a receiver is described in a French patent application filed by the present applicant on Mar. 24, 1998, under number 98 03586.

FIG. 13 schematically illustrates such a receiver. As illustrated, it comprises a general input E, receiving a composite signal R(t), K parallel channels V₁, V₂, . . . , V_(K), where K is the maximum number of users, each channel delivering a signal R₁(T), R₂(T), R_(K)(T), specific to each user, a weighted interference parallel suppression circuit (SPIP) and K decision circuits D₁, D₂, . . . , D_(K), delivering data d₁, d₂, . . . , d_(K), specific to each of the users.

Finally FIG. 14 enables the performances of a receiving method according to the invention to be compared with conventional methods. This FIG. 13 shows the variations of the bit error rate (BER) versus the signal to noise ratio SNR. FIG. 13 makes the assumption of K=5 users with N=63. The Doppler effect was simulated by a shift with respect to the carrier of the local oscillator.

Curve 50 refers to a conventional method with one stage, without interference suppression. Curves 51 and 52 refer to the same method but with two different Doppler effects, the first with a relative shift of 10⁻⁶ at 2.45 GHz and the second with a relative shift of 10⁻⁵.

Curve 60 refers to an interference parallel suppression method with only one stage for parallel suppression of interferences and curves 61, 62 to the same method but with shifts of 10⁻⁶ and 10⁻⁵.

Curve 70 refers to a method with two stages for parallel suppression of interferences with associated curves 71, 72 for shifts at 10⁻⁶ and 10⁻⁵.

Finally, curve 80 marks the theoretical limit of the phase difference modulation technique (DQPSK). 

1-5. (canceled)
 6. A system, comprising: a baseband signal generator capable of generating a baseband signal from a received signal, the received signal comprising a preamble comprising a portion of known symbols spread in frequency by a pseudo-random sequence of chips and a portion of information symbols spread in frequency by the pseudo-random sequence of chips, and the baseband signal further comprising a modulation related to a shift in frequency from a transmitted frequency of the received signal; a correlator capable of generating a correlation signal based on a correlation between the portion of information symbols of the baseband signal and the pseudo-random sequence, the correlation signal comprising at least one or more correlation components based on at least one of an in-phase component of the baseband signal and a quadrature component of the baseband signal; a DOT-signal generator capable of generating a DOT signal based on a sum of two direct products of successive samples of the correlation components; a CROSS-signal generator capable of generating a CROSS signal based on a difference between two crossed products of successive samples of the correlation components; a modulation estimator capable of generating an estimated signal based on a period of the modulation of the baseband signal related to the shift in frequency based on an inverse of an arctangent of a ratio between the CROSS signal and the DOT signal at at least one symbol period multiplied by π/2 times a number of chips in the at least one symbol period; and a frequency-shift corrector capable of correcting the modulation of the baseband signal related to the shift in frequency by correcting one of the baseband signal and the correlation signal based on the estimated signal.
 7. The system according to claim 6, further comprising: a lowpass filter capable of filtering at least one of the CROSS signal and the DOT signal.
 8. The system according to claim 6, wherein the frequency-shift corrector is further capable of forming a first component equal to cos(πx/2T) and a second component equal to sin(πx/2T), such that x is a unit of time equal to kN, k is a number of successive integer values and N is a number of chips of the pseudo-random sequence, and T is a modulation period.
 9. The system according to claim 8, wherein the baseband signal comprises an in-phase signal I_(dop) and an in-quadrature signal Q_(dop) each containing the modulation related to the shift in frequency from the transmitted frequency of the received signal, and wherein the frequency-shift corrector is capable of determining at least one of a first correction signal equal to: I _(dop) cos(πx/2T)+Q _(dop) sin(πx/2T), and a second correction signal equal to Q _(dop) cos(πx/2T)−I _(dop) sin(πx/2T), the frequency-shift corrector capable of generating a frequency-shift-corrected in-phase component of the baseband signal using the first correction signal, and capable of generating a frequency-shift-corrected in-quadrature component of the baseband signal.
 10. The system according to claim 8, wherein the frequency-shift corrector is capable of determining at least one of a first correction signal equal to: CORR_(dop)(I)cos(πx/2T)+CORR_(dop)(Q) sin(πx/2T), and a second correction signal equal to CORR_(dop)(Q)cos(πx/2T)−CORR_(dop)(I)sin(πx/2T), the frequency-shift corrector capable of generating a frequency-shift-corrected correlation signal CORR_(dop)(I) using the first correction signal, and capable of generating a frequency-shift-corrected correlation signal CORR_(dop)(Q).
 11. An apparatus, comprising: a first correlation circuit capable of generating a first correlation signal based at least in part on a received in-phase signal; a second correlation circuit capable of generating a second correlation signal based at least in part on a received in-quadrature signal; a differential demodulator capable of generating at least one of a DOT signal and a CROSS signal based at least in part on the first and second correlation signals; an estimation circuit capable of estimating a Doppler effect on at least one of the DOT signal and the CROSS signal; and a correction circuit capable of correcting the Doppler effect on only one of the DOT signal and the CROSS signal based on an inverse of an arctangent of a ratio between the CROSS signal and the DOT signal.
 12. An apparatus according to claim 11, wherein the correction circuit comprises: first and second multipliers capable of receiving a Doppler effect estimate on the DOT signal and the in-phase signal; a first adder capable of adding outputs of the first and second multipliers to generate a frequency-corrected in-phase signal; third and fourth multipliers capable of receiving a Doppler effect estimate on the CROSS signal and the in-quadrature signal; and a second adder capable of adding outputs of the third and fourth multipliers to generate a frequency-corrected quadrature signal.
 13. The apparatus according to claim 11, wherein the estimation circuit comprises: a ratio generator capable of generating an output related to a ratio between the CROSS signal and the DOT signal; a circuit capable of generating an output based on an arctangent from an output of the ratio generator; an inverse-tangent circuit capable of receiving the output of the ratio generator and capable of generating an output based on the inverse of the arctangent of the ratio between the CROSS signal and the DOT signal; and a generator circuit capable of receiving the output from the inverse-tangent circuit and capable of generating components of a correction signal based at least in part on the inverse arctangent.
 14. The apparatus according to claim 13, wherein the generator circuit is further capable of multiplying the output of the inverse-tangent circuit by π/2 times a number of chips in the estimated Doppler effect.
 15. A method, comprising: generating a baseband signal from a received signal, the received signal comprising a preamble comprising a portion of known symbols spread in frequency by a pseudo-random sequence of chips and a portion of information symbols spread in frequency by the pseudo-random sequence of chips, and the baseband signal further comprising a modulation related to a shift in frequency from a transmitted frequency of the received signal; generating a correlation signal based on a correlation between the portion of information symbols of the baseband signal and the pseudo-random sequence, the correlation signal comprising at least one or more correlation components based on at least one of an in-phase component of the baseband signal and a quadrature component of the baseband signal; generating a DOT signal based on a sum of two direct products of successive samples of the correlation components; generating a CROSS signal based on a difference between two crossed products of successive samples of the correlation components; generating an estimated signal based on a period of the modulation of the baseband signal related to the shift in frequency based on an inverse of an arctangent of a ratio between the CROSS signal and the DOT signal at at least one symbol period multiplied by π/2 times a number of chips in the at least one symbol period; and correcting the modulation of the baseband signal related to the shift in frequency by correcting one of the baseband signal and the correlation signal based on the estimated signal.
 16. The method according to claim 15, further comprising: filtering at least one of the CROSS signal and the DOT signal.
 17. The method according to claim 15, further comprising forming a first component equal to cos(πx/2T) and a second component equal to sin(πx/2T), such that x is a unit of time equal to kN, k is a number of successive integer values and N is a number of chips of the pseudo-random sequence, and T is a modulation period.
 18. The method according to claim 17, wherein the baseband signal comprises an in-phase signal I_(dop) and an in-quadrature signal Qd_(dop) each containing the modulation related to the shift in frequency from the transmitted frequency of the received signal, and the method further comprising: determining at least one of a first correction signal equal to: I _(dop) cos(πx/2T)+Q _(dop) sin(πx/2T), and a second correction signal equal to Q _(dop) cos(πx/2T)−I _(dop)sin(πx/2T); generating a frequency-shift-corrected in-phase component of the baseband signal using the first correction signal; and generating a frequency-shift-corrected in-quadrature component of the baseband signal.
 19. The method according to claim 17, further comprising determining at least one of a first correction signal equal to: CORR_(dop)(I)cos(πx/2T)+CORR_(dop)(Q)sin(πx/2T), and a second correction signal equal to CORR_(dop)(Q)cos(πx/2T)−CORR_(dop)(I)sin(πx/2T); generating a frequency-shift-corrected correlation signal CORR_(dop)(I) using the first correction signal; and capable of generating a frequency-shift-corrected correlation signal CORR_(dop)(Q).
 20. A method, comprising: generating a first correlation signal based at least in part on a received in-phase signal; generating a second correlation signal based at least in part on a received in-quadrature signal; generating at least one of a DOT signal and a CROSS signal based at least in part on the first and second correlation signals; estimating a Doppler effect on at least one of the DOT signal and the CROSS signal; and correcting the Doppler effect on only one of the DOT signal and the CROSS signal based on an inverse of an arctangent of a ratio between the CROSS signal and the DOT signal.
 21. A method according to claim 20, wherein further comprising: receiving a Doppler effect estimate on the DOT signal and the in-phase signal; generating a frequency-corrected in-phase signal; receiving a Doppler effect estimate on the CROSS signal and the in-quadrature signal; and generating a frequency-corrected quadrature signal.
 22. The method according to claim 20, further comprising: generating an output related to a ratio between the CROSS signal and the DOT signal; generating an output based on an arctangent from an output related to the ratio; generating an output based on the inverse of the arctangent of the ratio between the CROSS signal and the DOT signal; and generating components of a correction signal based at least in part on the inverse arctangent.
 23. The method according to claim 22, wherein further comprising multiplying the output of the inverse-tangent circuit by π/2 times a number of chips in the estimated Doppler effect. 